When we talk about a particle taking an infinite amount of time for it to cross the event horizon in the external observer's point of view, we assume that the particle follows a geodesic and does not affect the metric. However, if we assume the that the mass of the particle is not zero, it perturbs the metric a little. So, in theory, would the particle be able to enter the horizon in a finite time (for the external observer)?
I suspect the answer is yes because we have already simulations of Black hole mergers and they collide in a finite time span. We can think of one of the Black holes as a very massive particle since both particles and Black holes are point masses. Another example is that of a collapsing dust. We see again mass entering the horizon in a finite time span if the infalling mass can alter the geometry of space.
In addition, if one needed to calculate the trajectory of the infalling particle, how would he go about doing it? If we consider a point particle, there would be a singularity at the position of the particle and, as a result, we don't have any valid geodesics at the location of the particle.